Guiding functions and global bifurcation of periodic solutions of functional differential inclusions with infinite delay (Q388652)

The topological degree theory for multivalued maps and the method of guiding functions (see, e.g. [\textit{V. Obukhovskii} et al., Method of guiding functions in problems of nonlinear analysis. Lecture Notes in Mathematics 2076. Berlin: Springer (2013; Zbl 1282.34003)]) is applied to the study of bifurcations of periodic solutions for a family of functional differential inclusions in \(\mathbb{R}^n\) with infinite delay of the form NEWLINE\[NEWLINE x^{\prime}(t) \in F(t,x_t,\mu). NEWLINE\]NEWLINE The structure of a bifurcating branch of periodic solutions is described. An application to a feedback control system with infinite delay is given.